Induced-charge electrokinetic flows about polarizable nano-particles: the thick-Debye-layer limit

Using the standard weak-field approximation, we analyse the steady-state electrokinetic flow about an uncharged ideally polarizable spherical particle for the case of a Debye thickness which is large compared with the particle size. The dimensionless problem is governed by two parameters: beta, the applied field magnitude (normalized with the thermal scale), and lambda, the Debye thickness (normalized with particle size). The double limit beta << 1 and lambda >> 1 is singular, and the resolution of the flow field requires the use of inner-outer asymptotic expansions in the spirit of Proudman & Pearson (J. Fluid Mech., vol. 2, 1957, p. 237). Two asymptotic limits are identified: the 'moderately thick' limit beta lambda << 1, in which the outer domain is characterized by the Debye thickness, and the 'super-thick' limit beta lambda >> 1, in which the outer domain represents the emergence of electro-migration in the leading-order ionic-transport process. The singularity is stronger in the comparable two-dimensional flow about a circular cylinder, where a switchback mechanism in the moderately thick limit modifies the familiar O(beta(2)) leading-order flow to O(beta(2) In lambda).